The ratio of the volumes of two similar solids is proportional to the cube of the diameter - or of any other linear measurement. For example, at twice the diameter, you would have 8 times the volume.
64 729
If the ratio of side lengths is 49 (that is 49 to 1) then the ratio of their volumes is 493 to 1, which is 117,649 to 1.
4 to 1.
The ratio of the volumes of two similar spheres is the cube of the ratio of their radii. If the ratio of their radii is 59:1, then the ratio of their volumes is ( 59^3:1^3 ), which is ( 205379:1 ). Thus, the volume ratio of the two spheres is 205379:1.
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
64 729
A.9:36
64:729
125:216
If the ratio of side lengths is 49 (that is 49 to 1) then the ratio of their volumes is 493 to 1, which is 117,649 to 1.
4 to 1.
If the ratio is 2 : 7 then the volumes are in the ratio 8 : 343.
The ratio of the volumes of two similar spheres is the cube of the ratio of their radii. If the ratio of their radii is 59:1, then the ratio of their volumes is ( 59^3:1^3 ), which is ( 205379:1 ). Thus, the volume ratio of the two spheres is 205379:1.
The ratio of their volumes is 23^3 = 12167.
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
The corresponding sides of similar solids have a constant ratio.
If two cylinders are similar, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions. Given that the ratio of the altitudes (heights) of the cylinders is 2 to 3, the ratio of their volumes is ( \left(\frac{2}{3}\right)^3 = \frac{8}{27} ). Thus, the ratio of the volumes of the two cylinders is 8:27.